# B Would the velocity of a fluid increase right after exiting a pipe into open air?

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1. Apr 23, 2017

### dddoi

If you have an non-viscous incompressible fluid flowing in a pipe whose static pressure is higher than atmospheric pressure, then after exits the pipe will the dynamic pressure increase? The static pressure of the fluid right after exiting should decrease because it should be equal to the atmospheric pressure, so since the total pressure should stay the same the dynamic pressure would increase.

The increase in dynamic pressure implies an increase in the velocity the fluid, which seems to spell trouble because that would mean the flow rate inside the pipe is lower than the flow rate outside the pipe.

Any help would be greatly appreciated!

2. Apr 23, 2017

### Staff: Mentor

The static fluid pressure inside the pipe near its exit is atmospheric. What made you think that the static pressure is discontinous? Fluid pressure is a continuous function of spatial position.

3. Apr 23, 2017

### dddoi

My bad, my poor wording may have suggested that but I didn't think that. Regardless, doesn't the dynamic pressure near the exit still increase? A few centimeters from the end of the pipe, the static pressure is the atmospheric pressure so the dynamic pressure is higher, right? But in order for the volume flow rate to be the same there and somewhere inside the pipe, the cross-sectional area must be lower. The cross-sectional area doesn't seem to decrease, rather it increases which means my reasoning went awry somewhere but I can't see where.

4. Apr 24, 2017

### rcgldr

Assuming no losses in the system, such as friction within the pipe, and no changes in temperature, density, ... , and a pipe with constant cross sectional area, then mass flow and fluid velocity should be constant within the pipe. If the pressure decreases from above ambient to ambient near the end of the pipe, what accounts for the decrease in total energy as the fluid approaches the end of the pipe (where is that energy going)?

Can the mass flow be distributed over the cross sectional area so that some parts of the fluid move slower while other parts move faster, in such a manner that the overall mass flow remains constant, but the velocity distribution results in an increase in dynamic pressure while the static pressure decreases? For a fluid with no viscosity, I'm wondering if such a velocity distribution could be determined.

5. Apr 24, 2017

### Staff: Mentor

For an inviscid fluid, the pressure in the pipe is not decreasing along the pipe.
For an inviscid fluid, the velocity profile in the pipe is flat.

6. Apr 24, 2017

### dddoi

What about the velocity just outside the pipe? Is the higher because of the decrease in static pressure? Or is it the same?

7. Apr 24, 2017

### Staff: Mentor

As I said, the static pressure does not decrease. I don't know how may different ways there are to say this.

8. Apr 24, 2017

### rcgldr

I'm confused, assuming the static pressure within most of the pipe is greater than atmospheric, then where does the static pressure decrease to atmospheric, or is it impossible for an inviscid fluid to have a static pressure within the pipe greater than atmospheric ?

9. Apr 24, 2017

### Staff: Mentor

It's an impossible assumption because with invincible flow there can be no friction in a pipe, so no way for there to be a pressure gradient. But either way (even with viscous flow/drag), the pressure at the outlet is atmospheric.

10. Apr 24, 2017

### Staff: Mentor

Yes. It's impossible unless the pipe diameter is decreasing before the exit.

11. Apr 24, 2017

### rcgldr

With a viscous flow (at least on the part of the air outside the pipe), it would seem that the entrainment of the air just beyond the end of the pipe could cause the affected air's static pressure to go above atmospheric and return to ambient somewhere beyond the end of the pipe.

12. Apr 24, 2017

### Staff: Mentor

This effect would be very insignificant; I have never seen it included in the analysis of exit effects for viscous flow. For viscous flow, the main exit effect is the transition from the parabolic velocity profile inside the pipe to a flat velocity profile beyond the tube exit. This gives rise to an additional pressure drop, equivalent to an additional tube length on the order of about one tube diameter. Fluid inertia interacts with this and leads to the so-called vena contracta effect.

13. Apr 25, 2017

### rcgldr

Consider the case of a ducted fan with no taper in the tube (some model aircraft ducted fans are setup this way). My understanding is that the pressure in the tube ahead of the fan is lower than atmospheric and the pressure in the tube behind the fan is greater than atmospheric. The pressure in the tube would decrease due to friction, but unless the tube was fairly long, the pressure would remain above atmospheric until very near the end of the tube where the flow could get complicated (turbulent) due to interaction with the free stream air.

14. Apr 25, 2017

### Staff: Mentor

That's not what would happen. After the fan, the static pressure would decrease linearly from the value exiting the fan to atmospheric pressure at the tube exit.